Как найти sin 1000

The value of sin 1000 degrees is -0.9848077. . .. Sin 1000 degrees in radians is written as sin (1000° × π/180°), i.e., sin (50π/9) or sin (17.453292. . .). In this article, we will discuss the methods to find the value of sin 1000 degrees with examples.

• Sin 1000°: -0.9848077. . .
• Sin (-1000 degrees): 0.9848077. . .
• Sin 1000° in radians: sin (50π/9) or sin (17.4532925 . . .)

What is the Value of Sin 1000 Degrees?

The value of sin 1000 degrees in decimal is -0.984807753. . .. Sin 1000 degrees can also be expressed using the equivalent of the given angle (1000 degrees) in radians (17.45329 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1000 degrees = 1000° × (π/180°) rad = 50π/9 or 17.4532 . . .
∴ sin 1000° = sin(17.4532) = -0.9848077. . .

Explanation:

For sin 1000°, the angle 1000° > 360°. Given the periodic property of the sine function, we can represent it as sin(1000° mod 360°) = sin(280°). The angle 1000°, coterminal to angle 280°, is located in the Fourth Quadrant(Quadrant IV).
Since sine function is negative in the 4th quadrant, thus sin 1000 degrees value = -0.9848077. . .
Similarly, sin 1000° can also be written as, sin 1000 degrees = (1000° + n × 360°), n ∈ Z.
⇒ sin 1000° = sin 1360° = sin 1720°, and so on.
Note: Since, sine is an odd function, the value of sin(-1000°) = -sin(1000°).

Methods to Find Value of Sin 1000 Degrees

The sine function is negative in the 4th quadrant. The value of sin 1000° is given as -0.98480. . .. We can find the value of sin 1000 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 1000° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 1000 degrees as:

• ± √(1-cos²(1000°))
• ± tan 1000°/√(1 + tan²(1000°))
• ± 1/√(1 + cot²(1000°))
• ± √(sec²(1000°) — 1)/sec 1000°
• 1/cosec 1000°

Note: Since 1000° lies in the 4th Quadrant, the final value of sin 1000° will be negative.

We can use trigonometric identities to represent sin 1000° as,

• sin(180° — 1000°) = sin(-820°)
• -sin(180° + 1000°) = -sin 1180°
• cos(90° — 1000°) = cos(-910°)
• -cos(90° + 1000°) = -cos 1090°

Sin 1000 Degrees Using Unit Circle

To find the value of sin 1000 degrees using the unit circle, represent 1000° in the form (2 × 360°) + 280° [∵ 1000°>360°] ∵ sine is a periodic function, sin 1000° = sin 280°.

• Rotate ‘r’ anticlockwise to form a 280° or 1000° angle with the positive x-axis.
• The sin of 1000 degrees equals the y-coordinate(-0.9848) of the point of intersection (0.1736, -0.9848) of unit circle and r.

Hence the value of sin 1000° = y = -0.9848 (approx)

☛ Also Check:

• sin 360 degrees
• sin 15 degrees
• sin 135 degrees
• sin 21 degrees
• sin 14 degrees
• sin 910 degrees

FAQs on Sin 1000 Degrees

What is Sin 1000 Degrees?

Sin 1000 degrees is the value of sine trigonometric function for an angle equal to 1000 degrees. The value of sin 1000° is -0.9848 (approx).

What is the Value of Sin 1000 Degrees in Terms of Tan 1000°?

We know, using trig identities, we can write sin 1000° as tan 1000°/√(1 + tan²(1000°)). Here, the value of tan 1000° is equal to -5.671281.

What is the Exact Value of sin 1000 Degrees?

The exact value of sin 1000 degrees can be given accurately up to 8 decimal places as -0.98480775.

How to Find the Value of Sin 1000 Degrees?

The value of sin 1000 degrees can be calculated by constructing an angle of 1000° with the x-axis, and then finding the coordinates of the corresponding point (0.1736, -0.9848) on the unit circle. The value of sin 1000° is equal to the y-coordinate (-0.9848). ∴ sin 1000° = -0.9848.

How to Find Sin 1000° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 1000° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(1000°))
• ± tan 1000°/√(1 + tan²(1000°))
• ± 1/√(1 + cot²(1000°))
• ± √(sec²(1000°) — 1)/sec 1000°
• 1/cosec 1000°

☛ Also check: trigonometry table

Summary :

The sin trigonometric function to calculate the sin of an angle in radians,
degrees or gradians.

sin online

Description :

Sine function

The calculator allows to use most of the trigonometric functions, it is possible to calculate the
sine,
the cosine
and the tangent
of an angle through the functions of the same name..

The trigonometric function sine noted sin,
allows to calculate
the sine of an angle online , it is possible to use different angular units :
degree, grade and radians wich is the angular unit by default.

Calculation of the sine

Sine calculating an angle in radians

The sine calculator allows through the sin function to calculate
online the sine sine of an angle in radians, you must first
select the desired unit by clicking on the options button calculation module.
After that, you can start your calculations.

To calculate sine online of `pi/6`, enter
sin(`pi/6`), after calculation, the result
`1/2` is returned.

Note that the sine function is able to recognize some special angles and make the
calculations with special associated values in exact form.

Calculate the sine of an angle in degrees

To calculate the sine of an angle in degrees, you must first select the desired unit
by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 90, enter sin(90), after calculation, the
restults 1 is returned.

Calculate the sine of an angle in gradians

To calculate the sine of an angle in gradians, you must first select the desired unit
by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 50, enter sin(50), after computation,
the result `sqrt(2)/2` is returned.

Note that the sine function is able to recognize some special angles and do the
calculus with special associated exact values.

Special sine values table

The sine admits some special values which the calculator is able to determine in exact forms. Here is a table of
the commonsine values:

sin(`2*pi`)	`0`
sin(`pi`)	`0`
sin(`pi/2`)	`1`
sin(`pi/4`)	`sqrt(2)/2`
sin(`pi/3`)	`sqrt(3)/2`
sin(`pi/6`)	`1/2`
sin(`2*pi/3`)	`sqrt(3)/2`
sin(`3*pi/4`)	`sqrt(2)/2`
sin(`5*pi/6`)	`1/2`
sin(`0`)	`0`
sin(`-2*pi`)	`0`
sin(`-pi`)	`0`
sin(`pi/2`)	`-1`
sin(`-pi/4`)	`-sqrt(2)/2`
sin(`-pi/3`)	`-sqrt(3)/2`
sin(`-pi/6`)	`-1/2`
sin(`-2*pi/3`)	`-sqrt(3)/2`
sin(`-3*pi/4`)	`-sqrt(2)/2`
sin(`-5*pi/6`)	`-1/2`

Main properties

`AA x in RR, k in ZZ`,

• `sin(-x)= -sin(x)`
• `sin(x+2*k*pi)=sin(x)`
• `sin(pi-x)=sin(x)`
• `sin(pi+x)=-sin(x)`
• `sin(pi/2-x)=cos(x)`
• `sin(pi/2+x)=cos(x)`

Derivative of sine

The derivative of the sine is equal to cos(x).

Antiderivative of sine

The antiderivative of the sine is equal to -cos(x).

Properties of the sine function

The sine function is an odd function, for every real x, `sin(-x)=-sin(x)`.
The consequence for the curve representative of the sine function is that it admits the origin of the reference point as point of symmetry.

Equation with sine

The calculator has a solver which allows it to solve

equation with sine
of the form cos(x)=a.
The calculations to obtain the result are detailed, so it will be possible to solve equations like

`sin(x)=1/2`

or

`2*sin(x)=sqrt(2)`

with the calculation steps.

Syntax :

sin(x), where x is the measure of an angle in degrees, radians, or gradians.

Examples :

sin(`0`), returns 0

Derivative sine :

To differentiate function sine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the sine function

The derivative of sin(x) is derivative(`sin(x)`)=`cos(x)`

Antiderivative sine :

Antiderivative calculator allows to calculate an antiderivative of sine function.

An antiderivative of sin(x) is antiderivative(`sin(x)`)=`-cos(x)`

Limit sine :

The limit calculator allows the calculation of limits of the sine function.

The limit of sin(x) is limit(`sin(x)`)

Inverse function sine :

The inverse function of sine is the arcsine function noted arcsin.

Graphic sine :

The graphing calculator is able to plot sine function in its definition interval.

Property of the function sine :

The sine function is an odd function.

Calculate online with sin (sine)